Geodesic
A Method of Deducing $L$-Polyhedra for $n$-Lattices
Matematičeskie zametki, Tome 68 (2000) no. 6, pp. 830-841.

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We suggest a method for selecting an $L$-simplex in an $L$-polyhedron of an $n$-lattice in Euclidean space. By taking into account the specific form of the condition that a simplex in the lattice is an $L$-simplex and by considering a simplex selected from an $L$-polyhedron, we present a new method for describing all types of $L$-polyhedra in lattices of given dimension $n$. We apply the method to deduce all types of $L$-polyhedra in $n$-dimensional lattices for $n=2,3,4$, which are already known from previous results. 
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E. P. Baranovskii; P. G. Kononenko. A Method of Deducing $L$-Polyhedra for $n$-Lattices. Matematičeskie zametki, Tome 68 (2000) no. 6, pp. 830-841. http://geodesic.mathdoc.fr/item/MZM_2000_68_6_a2/

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